Automatic ENT Surgery Preplanning Using a Backtracking Maze Problem Solution

ABSTRACT

A method, consisting of receiving a computerized tomography scan of at least a part of a body of a patient, and identifying voxels of the scan that correspond to regions in the body that are traversable by a probe inserted therein. The method also includes displaying the scan on a screen and marking thereon selected start and termination points for the probe. A processor finds a path from the start point to the termination point consisting of a connected set of the identified voxels. The processor also uses the scan to generate a representation of an external surface of the body and displays the representation on the screen. The processor then renders an area of the external surface surrounding the path locally transparent in the displayed representation, so as to make visible on the screen an internal structure of the body in a vicinity of the path.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication 62/209,946, filed Aug. 26, 2015, which is incorporatedherein by reference.

FIELD OF THE INVENTION

This invention relates generally to surgery, and specifically topreplanning of invasive nasal sinus surgery.

BACKGROUND OF THE INVENTION

The paranasal sinuses comprise four separate pairs of three-dimensional(3D) air-filled spaces which are in proximity to the nasal cavity.Invasive surgery of a selected region of the sinuses may be considerednecessary, for example, in the case of severe sinusitis, using acatheter to reach the region. Typically, at present, prior to performingsuch invasive surgery, a computerized tomography (CT) scan of a selectedregion of one of the sinuses and its environs is taken. A physiciananalyzes the scan in order to select the best path, typically theshortest path, from a nostril to the selected region to be taken by thecatheter.

The selection of the best path is not a trivial operation. The sinusesare 3D spaces, and, especially if there is any sort of blockage betweena nostril and the selected region, the best path may comprise arelatively complicated route. In addition, while the CT scan can be usedto generate 3D images, the analysis of such images, because they arethree-dimensional, is difficult and time-consuming.

U.S. Pat. No. 7,720,521 to Chang et al., whose disclosure isincorporated herein by reference, describes a system for performingimage guided interventional and surgical procedures, including variousprocedures to treat sinusitis and other disorders of the paranasalsinuses.

U.S. Pat. No. 8,160,676 to Gielen et al., whose disclosure isincorporated herein by reference, describes a method for planning asurgical procedure. The plan can include a path or trajectory to reach aselected target.

U.S. Patent Application 2008/0183073 to Higgins et al., whose disclosureis incorporated herein by reference, describes methods to assist inplanning routes through hollow, branching organs in patients to optimizesubsequent endoscopic procedures.

U.S. Pat. No. 8,116,847 to Gattani et al., whose disclosure isincorporated herein by reference, describes a method for calculating anoptimum surgical trajectory or path for displacing a surgical instrumentthrough the interior of the body of a patient.

Documents incorporated by reference in the present patent applicationare to be considered an integral part of the application except that, tothe extent that any terms are defined in these incorporated documents ina manner that conflicts with definitions made explicitly or implicitlyin the present specification, only the definitions in the presentspecification should be considered.

SUMMARY OF THE INVENTION

An embodiment of the present invention provides a method, including:

receiving a computerized tomography (CT) scan of at least a part of abody of a patient;

identifying voxels of the scan that correspond to regions in the bodythat are traversable by a probe inserted therein;

displaying the scan on a screen and marking thereon selected start andtermination points for the probe;

finding a path from the start point to the termination point comprisinga connected set of the identified voxels;

using the scan to generate a representation of an external surface ofthe body and displaying the representation on the screen; and

rendering an area of the external surface surrounding the path locallytransparent in the displayed representation, so as to make visible onthe screen an internal structure of the body in a vicinity of the path.

Typically, identifying the voxels of the scan includes selecting mucousas a traversable species. Alternatively or additionally, identifying thevoxels of the scan includes identifying soft tissue as a traversablespecies. Further alternatively or additionally identifying the voxels ofthe scan includes defining a range of Hounsfield units for voxels.

In a disclosed embodiment finding the path includes ensuring that noportion of the path includes a radius of curvature smaller than a rangeof possible radii of curvature of the probe.

In a further disclosed embodiment finding the path includes ensuringthat a path diameter is always larger than a diameter of the probe.

In a yet further disclosed embodiment, finding the path includes findinga shortest path from the start point to the termination point.Typically, finding the shortest path includes using Dijkstra's algorithmor an extension thereof.

In an alternative embodiment finding the path includes ensuring that theprobe is not required to traverse a portion of the path having a pathradius curvature smaller than a probe radius of curvature achievable atthe portion.

In a further alternative embodiment receiving the CT scan includesreceiving one of an X-ray CT scan and a magnetic resonance imaging CTscan.

There is further provided, according to an embodiment of the presentinvention, apparatus, including:

a screen configured to display a computerized tomography (CT) scan of atleast a part of a body of a patient; and

a processor configured to:

receive the scan,

identify voxels of the scan that correspond to regions in the body thatare traversable by a probe inserted therein,

mark on the screen selected start and termination points for the probe,

find a path from the start point to the termination point comprising aconnected set of the identified voxels,

use the scan to generate a representation of an external surface of thebody and display the representation on the screen, and

render an area of the external surface surrounding the path locallytransparent in the displayed representation, so as to make visible onthe screen an internal structure of the body in a vicinity of the path.

The present disclosure will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a nasal sinus surgery system,according to an embodiment of the present invention;

FIG. 2 is a flowchart showing steps of a surgery pre-planning componentof the system, according to an embodiment of the present invention; and

FIGS. 3-8 are diagrams illustrating the steps of the flowchart,according to an embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS Overview

Embodiments of the present invention assist a physician, byautomatically selecting in a surgery pre-planning procedure the bestpath to be taken by a catheter, and by displaying the selected path onan image of the patient. The patient image is based on the region of thepatient where the procedure is to be performed.

A computerized tomography (CT) scan, typically an X-ray CT scan, of theprocedure region is received, and voxels of the scan corresponding toregions of the body of the patient that are traversable by a probe to beinserted into the patient are identified. The identification istypically by defining a range of Hounsfield units for the voxels.

The physician displays the scan on a screen, and marks on the scan startand termination points for the probe.

A processor uses an algorithm, such as Dijksbra's algorithm, to find apath, typically the shortest path, from the start point to thetermination point that has a connected set of the identified voxels.

The processor also generates a representation of an external surface ofthe body and the representation is displayed on the screen. Theprocessor then renders an area of the external surface surrounding thepath locally transparent in the displayed representation, so as to makevisible on the screen an internal structure of the body in a vicinity ofthe path.

DETAILED DESCRIPTION

Reference is now made to FIG. 1, which is a schematic illustration of anasal sinus surgery system 20, according to an embodiment of the presentinvention. System 20 is typically used during an invasive procedure on anasal sinus of a patient 22, and the system includes a surgerypre-planning component, described in more detail below.

For the actual procedure, a set of magnetic field generators 24 may befixed to the head of the patient, for example by incorporating thegenerators into a frame which is clamped to the patient's head. Thefield generators enable the position of a probe 28 that is inserted intothe nasal sinus of the patient to be tracked. A system using magneticfield generators, such as generators 24, for tracking an entity insertedinto a patient is described in U.S. patent application Ser. No.14/792,823, to Govari et al., which is incorporated herein by reference.In addition, the Carto® system produced by Biosense Webster, of DiamondBar, Calif., uses a tracking system similar to that described herein forfinding the location and orientation of a coil in a region irradiated bymagnetic fields.

Elements of system 20, including generators 24, may be controlled by asystem processor 40, comprising a processing unit communicating with oneor more memories. Processor 40 may be mounted in a console 50, whichcomprises operating controls 51 that typically include a keypad and/or apointing device such as a mouse or trackball. Console 50 also connectsto other elements of system 20, such as a proximal end 52 of probe 28. Aphysician 54 uses the operating controls to interact with the processorwhile performing the procedure, and the processor may present resultsproduced by system 20 on a screen 56.

Processor 40 uses software stored in a memory of the processor tooperate system 20. The software may be downloaded to processor 40 inelectronic form, over a network, for example, or it may, alternativelyor additionally, be provided and/or stored on non-transitory tangiblemedia, such as magnetic, optical, or electronic memory.

FIG. 2 is a flowchart showing steps of the surgery pre-planningcomponent referred to above, and FIGS. 3-8 are diagrams illustrating thesteps, according to an embodiment of the present invention. Thepre-planning component described by the flowchart is typicallyimplemented prior to performance of the invasive surgery procedure onpatient 22, and determines an optimal path to be followed by invasiveprobe 28 in the procedure. The pre-planning is assumed to be performedby physician 54.

In an initial step 100 of the flowchart, a computerized tomography (CT)X-ray scan of the nasal sinuses of patient 22 is performed, and the datafrom the scan is acquired by processor 40. As is known in the art, thescan comprises two-dimensional X-ray “slices” of the patient, and thecombination of the slices generates three-dimensional voxels, each voxelhaving a Hounsfield unit, a measure of radiodensity, determined by theCT scan.

In an image generation step 102, physician 54 displays results of thescan on screen 56. As is known in the art, the results may be displayedas a series of two-dimensional (2D) slices, typically along planesparallel to the sagittal, coronal, and/or transverse planes of patient22, although other planes are possible. The direction of the planes maybe selected by the physician.

The displayed results are typically gray scale images, and an example isprovided in FIG. 3, which is a slice parallel to the coronal plane ofpatient 22. The values of the gray scales, from black to white, may becorrelated with the Hounsfield unit (HU) of the corresponding voxels, sothat, as applies to the image of FIG. 3, air having HU=−1000 may beassigned to be black, and dense bone having HU=3000 may be assigned tobe white.

As is known in the art, apart from the values for air and water, whichby definition are respectively −1000 and 0, the value of the Hounsfieldunit of any other substance or species, such as dense bone, isdependent, inter alia, on the spectrum of the irradiating X-rays used toproduce the CT scans referred to herein. In turn, the spectrum of theX-rays depends on a number of factors, including the potential in kVapplied to the X-ray generator, as well as the composition of the anodeof the generator. For clarity in the present disclosure, the values ofHounsfield units for a particular substance or species are assumed to beas given in Table I below.

TABLE I Species/Substance Hounsfield Unit Air −1000 Soft Tissue −300 to−100 Fat  −50 Water   0 Blood +30 to +45 Dense Bone +3000

However the numerical values of HUs for particular species (other thanair and water) as given in Table I are to be understood as being purelyillustrative, and those having ordinary skill in the art will be able tomodify these illustrative values, without undue experimentation,according to the species and the X-ray machine used to generate the CTimages referred to herein.

Typically, a translation between HU values and gray scale values isencoded into a DICOM (Digital Imaging and Communications in Medicine)file that is the CT scan output from a given CT machine. For clarity inthe following description the correlation of HU=−1000 to black, andHU=3000 to white, and correlations of intermediate HU values tocorresponding intermediate gray levels is used, but it will beunderstood that this correlation is purely arbitrary. For example, thecorrelation may be “reversed,” i.e., HU=−1000 may be assigned to white,HU=3000 assigned to black, and intermediate HU values assigned tocorresponding intermediate gray levels. Thus, those having ordinaryskill in the art will be able to adapt the description herein toaccommodate other correlations between Hounsfield units and gray levels,and all such correlations are assumed to be comprised within the scopeof the present invention.

In a marking step 104 the physician marks an intended start point, wherehe/she will insert probe 28 into the patient, and an intended targetpoint, where the distal end of the probe is to terminate. The two pointsmay be on the same 2D slice. Alternatively, each point may be on adifferent slice. Typically, both points are in air, i.e., whereHU=−1000, and the termination point is usually, but not necessarily, ata junction of air with liquid or tissue shown in the slice. (An examplewhere the termination point is not at such a junction is when the pointmay be in the middle of an air-filled chamber.) FIG. 4 illustrates astart point 150 and a termination point 152 that are marked on the same2D slice by the physician, and for clarity these points are assumed,except where otherwise stated, to be the points used in the remainingdescription of the flowchart. Typically the start and termination pointsare displayed in a non-gray scale color, for example, red.

In a permissible path definition step 106, the physician defines rangesof Hounsfield units which the path finding algorithm, referred to below,uses as acceptable voxel values in finding a path from start point 150to termination point 152. The defined range typically includes HUs equalto −1000, corresponding to air or a void in the path; the defined rangemay also include HUs greater than −1000, for example, the range may bedefined as given by expression (1):

{HU|−1000≦HU≦U}  (1)

where U is a value selected by the physician.

For example U may be set to +45, so that the path taken may includewater, fat, blood, soft tissue as well as air or a void.

There is no requirement that the defined range of values is a continuousrange, and the range may be disjoint, including one or more sub-ranges.In some embodiments a sub-range may be chosen to include a specific typeof material. An example of a disjoint range is given by expression (2):

{HU|HU=−1000 or A≦HU≦B}  (2)

where A, B are values selected by the physician.

For example A, B may be set to be equal to −300 and −100 respectively,so that the path taken may include air or a void and soft tissue.

The method of selection for the range of HUs for the may be by anyconvenient method known in the art, including, but not being limited to,by number, and/or by name of material, and/or by gray scale. Forexample, in the case of selection by gray scale, physician 54 may selectone or more regions of the CT image, and the HU equivalents of the grayscale values of the selected regions are included in the acceptablerange of HUs for voxels of the path to be determined by the path findingalgorithm.

In the case of selection by name, a table of named species may bedisplayed to the physician. The displayed table is typically similar toTable I, but without the column giving values of Hounsfield units. Thephysician may select one or more named species from the table, in whichcase the HU equivalents of the selected named species are included inthe acceptable range of HUs for voxels of the path to be determined bythe path finding algorithm.

In a path finding step 108, processor 40 implements a path findingalgorithm to find one or more shortest paths, between start point 150and termination point 152, that is to be followed by probe 28. Thealgorithm assumes that traversable voxels in the path include any voxelshaving HUs in the HU range defined in step 106, and that voxels havingHU values outside this defined range act as barriers in any path found.While the path finding algorithm used may be any algorithm that is ableto determine a shortest path within a three-dimensional maze, theinventors have found that the Flood Fill algorithm, Dijkstra'salgorithm, or an extension such as the A* algorithm, give better resultsin terms of speed of computation and accuracy of determining theshortest path than other algorithms such as Floyd's algorithm orvariations thereof.

In some embodiments, the path finding step includes taking account ofmechanical properties and dimensions of probe 28. For example, in adisclosed embodiment, probe 28 may be limited, when it bends, to a rangeof possible radii of curvature. In determining possible paths to befollowed by the probe, the processor ensures that no portion of the pathdefines a radius less than this range of radii.

In a further disclosed embodiment, the processor takes account of probemechanical properties that permit different portions of the probedifferent ranges of radii of curvature. For example, the end of apossible path may have a smaller radius of curvature than the possibleradii of curvature of a proximal part of the probe. However, the distalend of the probe may be more flexible than the proximal part, and may beflexible enough to accommodate the smaller radius of curvature, so thatthe possible path is acceptable.

In considering the possible radii of curvature of the probe, and thedifferent radii of curvature of possible paths, the processor takes intoaccount which portions of a path need to be traversed by differentportions of the probe, and the radii of curvature achievable by theprobe, as the distal end of the probe moves from start point 150 totermination point 152.

In a yet further disclosed embodiment, the processor ensures that a pathdiameter D is always larger than a measured diameter d of probe 28. Theconfirmation may be at least partially implemented, for example, by theprocessor using erosion/dilation algorithms, as are known in the art, tofind voxels within the ranges defined in step 106.

In an overlay step 110, the shortest path found in step 108 is overlaidon an image that is displayed on screen 56. FIG. 5 illustrates ashortest path 154, between start point 150 and termination point 152,that has been overlaid on the image of FIG. 4. Typically path 154 isdisplayed in a non-gray scale color, which may or may not be the samecolor as the start and termination points. In the case that step 108finds more than one shortest path, all such paths may be overlaid on theimage, typically in different non-gray scale colors.

Typically the path found traverses more than one 2D slice, in which casethe overlaying may be implemented by incorporating the path found intoall the 2D slices that are relevant, i.e., through which the pathtraverses. Alternatively or additionally, an at least partiallytransparent 3D image may be generated from the 2D slices of the scan,and the path found may be overlaid on the 3D image. The at leastpartially transparent 3D image may be formed on a representation of anexternal surface of patient 22, as is described in more detail below.

FIG. 6 is a representation of an external surface 180 of patient 22,according to an embodiment of the present invention. Processor 40 usesthe CT scan data acquired in step 100 to generate the representation ofthe external surface, by using the facts that air has an HU value of−1000 while skin has an HU value significantly different from this. Byway of example, representation 180 is assumed to be formed on a planeparallel to the coronal plane of the patient, i.e., parallel to an xyplane of a frame of reference 184 defined by the patient, the axes ofwhich are also drawn in FIG. 6 and in FIG. 7 below.

FIG. 7 schematically illustrates a boundary plane 190 and a boundingregion 192, according to an embodiment of the present invention. Underdirections from physician 54, processor 40 delineates regions ofrepresentation 180 which are to be rendered transparent, and those whichare to be left “as is.” In order to perform the delineation, thephysician defines boundary plane 190, and bounding region 192 in theboundary plane, using a bounding perimeter 194 for the region.

For clarity, the following description assumes that the boundary planeis parallel to an xy plane of frame of reference 184, as is illustratedschematically in FIG. 7, and that it has an equation given by:

z=z _(bp)  (3)

As described below, processor 40 uses the boundary plane and thebounding region to determine which elements of surface 180 are to berendered locally transparent, and which elements are not to be sorendered.

Processor 40 determines elements of surface 180 (FIG. 6) having valuesof z≧z_(bp), and that, when projected along the z-axis, lie within area192. The processor then renders the elements transparent so that,consequently, these elements are no longer visible in surface 180. Forexample, in FIG. 7 a tip 196 of the nose of patient 22 has a valuez≧z_(bp), so a broken line 198 in the vicinity of the patient's nose tipillustrates parts of external surface 180 that are no longer visiblewhen the image of the surface is presented on screen 56.

In consequence of the above-defined elements being rendered transparent,elements of surface 180, having values of z≦z_(bp) and that whenprojected along the z-axis lie within area 192 are now visible, so aredisplayed in the image. Prior to the local transparent rendering, the“now visible” elements were not visible since they were obscured bysurface elements. The now visible elements include elements of shortestpath 154, as is illustrated in FIG. 8.

FIG. 8 schematically illustrates surface 180 as displayed on screen 56after the local transparency rendering of the elements of the surfacewithin area 170. For clarity a broken circle 194A, corresponding toperimeter 194 (FIG. 6) has been overlaid on the image, and frame ofreference 184 is also drawn in the figure. Because of the transparentrendering of elements within circle 194A, an area 200 within the circlenow shows internal structure, derived from the CT tomographic datareceived in step 100, of subject 22.

Shortest path 154 has also been drawn in FIG. 8. Because of thetransparent rendering of elements within circle 194A, a portion of thepath is now visible in the image of surface 180, and has been drawn as asolid while line 202. The portion of the path that is invisible, becauseit is hidden by elements of surface 180 that have not been renderedtransparent, is shown as broken white line 204.

It will be appreciated that in the case illustrated in FIGS. 6 and 8screen 56 is in an xy plane, so that the screen acts as a “virtualcamera” of a viewer looking towards surface 180 along a z axis.

The description above provides one example of the application of localtransparency to viewing a shortest path derived from tomographic data,the local transparency in this case being formed relative to a planeparallel to the coronal plane of the subject. It will be understood thatbecause of the three-dimensional nature of the tomographic data, thedata may be manipulated so that embodiments of the present invention mayview the shortest path using local transparency formed relative tosubstantially any plane through patient 22, and that may be defined inframe of reference 184.

In forming the local transparency, the dimensions and position of thebounding plane and the bounding region may be varied to enable thephysician to also view the shortest path, and internal structures in thevicinity of the path.

The physician may vary the direction of the bounding plane, for exampleto enhance the visibility of particular internal structures. While thebounding plane is typically parallel to the plane of the image presentedon screen 56, this is not a requirement, so that if, for example, thephysician wants to see more detail of a particular structure, she/he mayrotate the bounding plane so that it is no longer parallel to the imageplane.

In some cases the range of HU values/gray scales selected in step 106includes regions other than air, for example, regions that correspond tosoft tissue and/or mucous. The path found in step 108 may include suchregions, and in this case, for probe 28 to follow the path, theseregions may have to be cleared, for example by debriding. In an optionalwarning step 112, the physician is advised of the existence of regionsof path 154 that are not in air, for example by highlighting a relevantsection of the path, and/or by other visual or auditory cues.

While the description above has assumed that the CT scan is an X-rayscan, it will be understood that embodiments of the present inventioncomprise finding a shortest path using MRI (magnetic resonance imaging)tomography images.

Thus, referring back to the flowchart, in the case of MRI images,wherein Hounsfield values may not be directly applicable, in step 106the physician defines ranges of gray scale values (of the MRI images)which the path finding algorithm uses as acceptable voxel values infinding a path from the start point to the termination point. In step108, the path finding algorithm assumes that traversable voxels in thepath include any voxels having gray scales in the gray scale rangedefined in step 106, and that voxels having gray scale values outsidethis defined range act as barriers in any path found. Other changes tothe description above, to accommodate using MRI images rather than X-rayCT images, will be apparent to those having ordinary skill in the art,and all such changes are to be considered as comprised within the scopeof the present invention.

It will thus be appreciated that the embodiments described above arecited by way of example, and that the present invention is not limitedto what has been particularly shown and described hereinabove. Rather,the scope of the present invention includes both combinations andsubcombinations of the various features described hereinabove, as wellas variations and modifications thereof which would occur to personsskilled in the art upon reading the foregoing description and which arenot disclosed in the prior art.

1. A method, comprising: receiving a computerized tomography (CT) scanof at least a part of a body of a patient; identifying voxels of thescan that correspond to regions in the body that are traversable by aprobe inserted therein; displaying the scan on a screen and markingthereon selected start and termination points for the probe; finding apath from the start point to the termination point comprising aconnected set of the identified voxels; using the scan to generate arepresentation of an external surface of the body and displaying therepresentation on the screen; and rendering an area of the externalsurface surrounding the path locally transparent in the displayedrepresentation, so as to make visible on the screen an internalstructure of the body in a vicinity of the path.
 2. The method accordingto claim 1, wherein identifying the voxels of the scan comprisesselecting mucous as a traversable species.
 3. The method according toclaim 1, wherein identifying the voxels of the scan comprisesidentifying soft tissue as a traversable species.
 4. The methodaccording to claim 1, wherein identifying the voxels of the scancomprises defining a range of Hounsfield units for voxels.
 5. The methodaccording to claim 1, wherein finding the path comprises ensuring thatno portion of the path comprises a radius of curvature smaller than arange of possible radii of curvature of the probe.
 6. The methodaccording to claim 1, wherein finding the path comprises ensuring that apath diameter is always larger than a diameter of the probe.
 7. Themethod according to claim 1, wherein finding the path comprises findinga shortest path from the start point to the termination point.
 8. Themethod according to claim 7, wherein finding the shortest path comprisesusing Dijkstra's algorithm or an extension thereof.
 9. The methodaccording to claim 1, wherein finding the path comprises ensuring thatthe probe is not required to traverse a portion of the path having apath radius curvature smaller than a probe radius of curvatureachievable at the portion.
 10. The method according to claim 1, whereinreceiving the CT scan comprises receiving one of an X-ray CT scan and amagnetic resonance imaging CT scan.
 11. Apparatus, comprising: a screenconfigured to display a computerized tomography (CT) scan of at least apart of a body of a patient; and a processor configured to receive thescan, identify voxels of the scan that correspond to regions in the bodythat are traversable by a probe inserted therein, mark on the screenselected start and termination points for the probe, find a path fromthe start point to the termination point comprising a connected set ofthe identified voxels, use the scan to generate a representation of anexternal surface of the body and display the representation on thescreen, and render an area of the external surface surrounding the pathlocally transparent in the displayed representation, so as to makevisible on the screen an internal structure of the body in a vicinity ofthe path.
 12. The apparatus according to claim 11, wherein identifyingthe voxels of the scan comprises selecting mucous as a traversablespecies.
 13. The apparatus according to claim 11, wherein identifyingthe voxels of the scan comprises identifying soft tissue as atraversable species.
 14. The apparatus according to claim 11, whereinidentifying the voxels of the scan comprises defining a range ofHounsfield units for voxels.
 15. The apparatus according to claim 11,wherein finding the path comprises ensuring that no portion of the pathcomprises a radius of curvature smaller than a range of possible radiiof curvature of the probe.
 16. The apparatus according to claim 11,wherein finding the path comprises ensuring that a path diameter isalways larger than a diameter of the probe.
 17. The apparatus accordingto claim 11, wherein finding the path comprises finding a shortest pathfrom the start point to the termination point.
 18. The apparatusaccording to claim 17, wherein finding the shortest path comprises usingDijkstra's algorithm or an extension thereof.
 19. The apparatusaccording to claim 11, wherein finding the path comprises ensuring thatthe probe is not required to traverse a portion of the path having apath radius curvature smaller than a probe radius of curvatureachievable at the portion.
 20. The apparatus according to claim 11,wherein receiving the CT scan comprises receiving one of an X-ray CTscan, a magnetic resonance imaging CT scan.